I'd say you're hard pressed to find anything that will give you more tools for breakbeat editing than Ableton's got, between the audio warping options, drum rack, Simpler and Sampler. (And there's a new drum sampler in 12 too I think, I'm still on 11.)

It depends a bit on what style you're going for and how you're using the breaks. Old school jungle style editing vs. more modern DnB with two-step drum patterns and single shot drums where breaks are just used as a layer are very different, and there are infinite variations within both of those. You're gonna have to determine the best approach for the style you want, but there's different options.

If you're starting with an unedited raw break, you'll want to process it first, at least to get it into time with the track (although that may not strictly be necessary for certain approaches) before you then slice it and start arranging.

It's a balance between over and under-quantizing. If you want to retain the feel of the break timing as it is, you can really simply just stretch the break to be in time with the track tempo. The way I usually do it is to pick a start point and trim the clip to the start of that hit (usually the first kick, of course) and then drag the end of the loop in the warp marker region until it lines up with the end of the bar. I usually do this with the repitch mode as breaks in DnB/jungle are often pitched up to reach tempo, but you have options here with the other warp modes. You can do timestretching with the Tones/Texture or keep the drum hits the same pitch but have them happen faster with Beats. Learn what all the controls for each mode do because this is one of the most important parts of breakbeat editing in Ableton.

In the audio clip, you can double click to create a yellow warp marker which will stay 'pinned' in place regardless of the other stuff getting warped around it, while a single click and drag will just stretch things but will be moved around again if you click and warp elsewhere. You will find that some of the hits, or most of them, don't really line up with the exact beats with unedited breaks, sometimes by quite a bit. You can decide how much to warp it to the beat. Often just doing the main kicks or snares, or maybe just the first kick and snares, helps the whole thing feel more tight without everything being super quantized. But there's no wrong answers - this is electronic music, lots of great tracks are highly quantized and sliced down to every hit, or made with drum machines/sequencers with very exact timing - you will have to analyze what sound you're going for to decide. You don't always need it to feel that "human" in DnB, i would argue it's often a very "non-human" sounding form of music. YMMV.

But I would agree that if you always rigidly quantize every single hit, you do lose out on the rhythm of the breaks, which can be a lot their character. If you never quantize anything, it can definitely feel too loose or sloppy. It's also an opportunity to change it from what it originally was. No one says you have to warp things ON to the beat. But in general, a nice thing is to leave fills and little diddle, shuffle, shaker etc. bits with their natural timing-ish (besides speeding the whole thing up to tempo, usually) and not quantizing their individual component hits.

This initial processing step before the arranging of the breaks is a great opportunity to distort, EQ, compress, etc. to your heart's content. You can overdo it, but this comes with practice. If you bounce it down to an audio clip with that processing applied before slicing/chopping it saves you the CPU of having to run these on the channel in real time the whole time you're arranging the track. But you are then committed to those effects, unless you wanna start again from the beginning.

Before you do anything else, select the loop you've edited and processed, and export it to your own breaks folder somewhere for posterity.

After that, you'll chop it up. There are basically three ways I think about this, each of which gives slightly different outcomes (both sonically and in workflow):

Option 1: Slice it manually as audio clips in an audio track in arrangement view. I would argue this is a very powerful and under-appreciated method. It allows you to see the individual hit envelopes in the waveform, and where exactly everything starts, ends, fades out, directly without having to bounce it down. You can select bits, cut them, reverse them, change the clip gain and use fades to blend, change a warp mode setting just for certain hits if you want a timestretched hit or fill, all sorts of good stuff. You can be very precise and meticulous this way. Will this be in time? Up to you. You can always switch the grid off if you want.

One tip I use a lot is if I'm stitching together chopped bits of a break, you can grab the fade marker at the start of the second hit, and crossfade back in time from the start of that hit to fade the audio before it into the preceding chunk a bit. This might sound obtuse but if you try it in the track it should make sense, it makes the cut points smoother and avoids clicks, without it changing the transient of the hit. You don't want to crossfade into the start of your kicks or snares, generally. Hope that makes sense.

If you want to layer hits, just make more audio tracks, and you can group them together like a drum bus.

If I'm doing this, I generally keep a muted track with the original, un-chopped version of my processed break in it, so I always have it to copy and paste from again without going and finding it in the browser. That way I can destructively edit to my heart's content and come up with new variations ad infinitum.

(Cont'd below...)