Flavio, I think you might be getting confused.
If you mean internal pedal effects, with the TL desktop, TLLE, TLSE and TLST you can select one pedal effect from the pedal section. With the TLEX, you have a second pedal section and can use one from each section at the same time. In addition, TLEX has an extra feature - a set of 11 stand alone distortion pedals (Tone Drive, Brit Lead, Fat Dist, Metal Dist, Rock Planet, Tube DX, Big Fuzz, VOX Tone Bender, Octa Fuzz, Techno Fuzz, Crusher) - but these are only available INSTEAD of the amp modeling ie if you select one of these, you can't select an amp model at the same time.
If you mean external stomp pedals, there's nothing to stop you using external pedals with any of the TL series; although TLSE and TLLE are more flexible here in that these have an FX loop that TLST and TLEX don't have.
Re MIDI, TL desktop, TLSE and TLLE have MIDI connectivity; TLST and TLEX do not. But I don't understand what you mean by 'storing settings of the amp on it' '?
Although I did like the TLEX, there are quite a few reasons why I decided against buying one (but I should stress that these are from a gigging rather than 'bedroom' playing perspective, and are geared around my personal needs and preferences):
For me (& I accept others may not find it a problem) one very awkward feature of the TLEX is that I have to press TWO switches simultaneously to go into 'stomp mode' which I found really clumsy for fast changing e.g. at a gig. I can do this with one pedal press in my VC12, and similarly it needs just one pedal press in the TLSE and TLLE.
The TLEX still has no patch naming facilities - 100 user and 100 factory pre-sets is great, but I can't remember what they are.
With TLLE and TLSE I can change the pedal order, which I can't do with TLST/TLEX.
TLLE/TLSE have an FX loop; TLST/TLEX do not.
Both the TLSE and TLLE offer a much larger choice of delays and reverbs than the TLST/TLEX, and you have significantly wider parameter control of effects.
TLLE/TLSE have MIDI connectivity; TLST/TLEX do not.
Whilst I accept the TLST was designed as a basic pedal that was light & compact, and I like the modeling in the TLST/TLEX, the TLEX is very much a stripped down version of the TLSE and TLLE that unfortunately just doesn't suit my needs.
Because of the above, I'm looking for a TLSE or TLLE - still not quite decided on which yet. The TLSE's additional advantages are its channel A/B switching and second expression pedal - but its disadvantage is physical size & weight. However, in many ways I think the TLSE may arguably have been the best Tonelab Vox ever made.