i was about to say wampler euphoria myself (set to smooth mode) because i personally use it too. but curiousdcat is correct to say that tone-wise, you can get close with some pedals, but you cant have the same feel of power amp clipping and speaker compression.
also consider that these pros play very loud in their venues, and the loud volume creates feedback that definitely affects the tone and sustain. this is something that can never be done in low volume.