I had one for a few days. It kicks ass. But, I returned it because I am a tweaker and quickly realized that I would spend way too much time experimenting and not playing. Also, the price tag is way too high for just bass because there is only one amp and cab sim. I didn't really care for the cab sim. The unit does so much and does it well but, I just found it easier to walk up to my amp, turn a few knobs and be done with it. Great unit though.
[Quick clarification: the AxeFx Ultra and AxeFxII have the following dedicated bass amp models: Ampeg SVT, Fender Bassman. Also, many other guitar amp models can be used with excellent results depending on the type of sound you're going for. The preamping capabilities of the unit are unrivaled IMO, so the best guide should always be your ears. There are also many bass cabinet emulations to choose from. The AFXII has quite a few bass cabinet IRs (Impulse Responses) of 15", 4x10, 8x10 cabinets, or you can even create your own IRs of your existing cabinets if you like. As with the amp models, you can also get excellent tones from some of the guitar cabinets. In addition, both units allow you to upload a number of third party cabinet impulses (Redwirez, Ownhammer, etc.), so there has never been a problem with limited choices, if variety is what you seek.
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I've been using the AxeFx Ultra/II for about 5 years. In short, it is a highly sophisticated, modern solution using arguably the best, most cutting edge technology available in a product of its type. Understand that the amps in the AxeFx are modeling algorithms, that exist in their own right. By contrast, the Kemper is a "profiler" which requires the use of a profile that is "captured" and then manipulated. Thus, you are at the mercy of the captured profile for base tone. With the AxeFx, you are at the mercy of the modeling algorithms for each amp as compiled by Fractal Audio's tech team, and these models are constantly being refined, upgraded, and expanded (free of cost).
For most typical bassists, the AxeFx is too much beast for the job, too many bells and whistles, and at too high a price tag. If you need only a basic "core" tone, and a multi-stomp or a couple of individual stomp boxes fulfill your needs for special effects, then you simply may not find value in the AxeFx. IMHO, it is not a matter of WHETHER a bassist could be made happy with the tones produced by the AxeFx, but rather, whether a bassist can personally, subjectively, justify the price tag.
If you're a tweaker and tinkerer, then the AxeFx is like an audio playground/Leggo/etch-a-sketch in a box. You can certainly focus more narrowly and use the unit as a simple preamp, a very high quality preamp, and not concern yourself with the vast breadth of features...this takes serious restraint, but many users are able.
If you're a "one trick pony" type of player - and there's nothing wrong with that! - then the AxeFx may be overkill at it's high price tag. If you enjoy stretching out, or have the NEED TO stretch out and can take advantage of the incredible versatility of the AxeFx, then you may find the price tag to be incredibly reasonable, and actually a money and back saver.
I'd be happy to answer any specific questions with respect to the AxeFx for bass. It is really a deep unit that can be successfully implemented in so many different ways. It's hard to boil it all down adequately and simply in a brief post.