I'd generally use the interface output since it is specifically designed for music production. Notebook manufacturers often cut corners to lower costs and the onboard sound card is probably nowhere near the specs of the 2i2.
However your headphones are low impedance so the notebook shouldn't have any problems driving a decent signal level, at least. It really depends on the specific onboard sound card you have, you'll have to compare it to the headphone output information listed at the bottom here:
https://us.focusrite.com/usb-audio-interfaces/scarlett-2i2

If you are getting a lot more bass with the notebook, check that the sound driver for the notebook sound adapter doesn't have some "Bass Boost" feature or something turned on by default.

Are you really @Dominik Lehmann with 577k SPI rank?

@Orrin Cummins, as far as I know impedance in 2i2 is fine, and 80 ohm phones are loud enough, especially compared to 250 ohm version. Can't really find any info about my onboard soundcard, thus it's hard to say what is it, but you're right, it shouldn't be better than 2i2. Yet, I encountered headphones amplifier in every studio I've been to, and wonder what's the point of it, if they usually have top interfaces for few grand... My laptop runs dolby audio (however stupid that sounds...) and it acctually has some bass boost, but does it work when I use the WASAPI driver in a DAW?
@Sergey Begaikin, yes I am indeed, I know the question is kinda lame, but better make sure I do everything right :D People learn all the time, don't they?
Cheers!

Then the answer is not so obvious. Any headphone amp initially developed to be flat across whole range. But USB powered soundcard really depends on USB port capacity. You need to use USB2.0 or USB3.0 port if it's possible with your notebook. Only these ports can provide enough current to feed headphone amp in Focusrite 2i2. USB3.0 is preferrable. I have mackie onyx blackjack powered by USB3.0 and 250Ohm Beyerdynamic version with fine frequency response. If the port USB1.1 is not your case then the @Orrin Cummins may be right. Just check the Focusrite soundcard properties. It depends on the OS version though.

To be sure about port capacity you can connect through the powered USB hub.

I have a 2i2 (2nd generation) and only ever go through it when recording. I do maybe 30-40% of my mixing in headphones and just plug my Sony MDR-7506 pair into the headphone input on my laptop.
I do use virtual room software when using headphones, namely Waves NX, which now has calibration for my headphones and a few others. I think the important thing is to get used to your monitoring setups and environments so you know them well. You mentioned that you noticed a difference in terms of bass with the 2 setups you're comparing, so that bodes really well and it might be just a case of which you prefer and/or which is more convenient.

I use USB 3.0, so that's not the case. Once tried virtual room, didn't like it tho, for me it just makes it weird, not better. And well, I own Beyer's cause they are supposed to be flat, and any soundcard's quirks would defeat the pourpose, woudln't it?
All in all, thank you guys for your response, I feel much more confident right now!

I would assume the built in DAC in your laptop would be lower quality than what's in your Focusrite.
More bass isn't necessarily a good thing. You're looking for the most even bass levels. The level where the bass sounds about as loud and even as the other frequencies in the spectrum.
Personally I would have the headphones connected to the interface.

Just another note: I actually own a 2i2, although I upgraded to a Scarlett 18i20 a few years ago. The audio quality of the Focusrite headphone outputs seemed fine but they weren't powerful enough to give me sufficient volume in my 300-Ohm HD600s, so I picked up this which I can highly recommend if you ever end up needing to use some higher-impedance headphones:
https://www.jdslabs.com/products/35/objective2-headphone-amplifier/

Norm, I didn't say more bass is a good thing, and frankly, isn't also a bad thing neither, my point is: is it TRUE sounding? I mean, if I mixed a song on a headphones and than would listen to it on a radio, would the bass be a) overwhelming, b) tiny, c) just as I mixed it?
I just want to be sure that my soundcard (or interface) isn't changing the frequency range I hear. But thanks for the answer though, really appreaciate that!

You might be able to get a definitive answer by doing a sine sweep using something like Room EQ wizard, with a loopback cable between headphone output and jack input. If you did that with both outputs and saw a difference in frequency response, then you'd have your answer :)
Instinctively though, I'd be more inclined to trust the Focusrite than an onboard soundcard, simply because the former is targeted at the producer market and the latter at the consumer market, and we know which of those demographics likes excess bass more ;) I don't think the 2i2 would be such a well-regarded interface if it coloured the sound to such an extent.

To have a true sounding you need to use equipements which will give a sound as flat as possible in the audio frequency bandwidth. The Focusrite should give you a better flat response than the laptop soundcard.
Your soundcard shouldn't change the frequency response but different headphones will change it. If you listen to your mixing on different radios, most of the time the bass will be overhelming or tiny and rarely as you mixed it. It depends of the type of transmission (FM/DAB+/Webcast/Type of codec) and the characteristics and parameters of the consumer's equipment.
About mastering: Bob Katz - Mastering Audio the art and the science

Hi,
Dominik Lehmann. I guess my comment wasn't very clear. Having more (or less) bass doesn't mean you are hearing accurate levels of bass. As i was saying you want to hear a flat response across the frequency spectrum. I was pretty much saying the same as you said in your reply. :)
Mike has the right answer on how to test. You can also do the same thing but use an SPL meter to measure the output in different frequency octaves.
Also I guess in the end you could just do a mix down on the speakers and then play the resulting audio in other environments and see if you have too much, too little, or just the right amount of bass.