Is there actually a difference?

As a former commercial property appraiser, I appraised 17 sound studios in Southern California.  Many of the studios had high end playback gear.  Same with my friend Robert Pincus, record producer, who visited various major label studios.  They did not use junk pro gear equipment in the 80s or 90s.  Two studios used my Legacy Focus for playback. Sony used big B&W800d2 for playback in NY.  I didn't check their cabling which was probably standard issue balanced and heavy duty A/C.  Most of the studios had superior power conditioning.  I remember one had 22 isolation transformers of 2KV each (former use was for tube computer equipment for BofA accounting).  

No, no, no.  Amps can be level matched and sound totally different.  The amps have to match the requirements of the speaker.  If the amps sound the same (possibly Harbeth), then the speaker is probably an easy load.  My speakers sound vastly different as do many high end speakers based on the amplifier's characteristics.  Difficult load speakers due to impedance, phase angles or sensitivity present all types of challenges for amplifiers.  

Ha Ha! Yes, imagine someone believing all speakers which measure the same sound the same.  There are intangible characteristics which are not necessarily measurable that make a difference.

smrex13  My experience in my large listening room with the Legacy Focus speakers (efficient with a low impedance load) includes an EAR 890 amp which cannot play dynamically or bass (yet does fine on Legacy Signature IIIs with an easier impedance maybe due to 3-10" instead of 3-12" woofers).  I currently use a pair of 125w. Class A/B monoblocks which is overkill.  However, I also have used a 35w. modified Dynaco Stereo 70 to great result (it is not ultralinear but voltage regulated design using a different tap off the transformer just like the monoblocks).  It has tremendous bass and dynamics.  It also has more neg. feedback and is less detailed than the monoblocks which is why it is used on the Signature IIIs.  So you're correct that the amp that can offer high current even at low power can really drive an efficient speaker with low impedance.  I've also tried a big Counterpoint hybrid amp (forgot which one, maybe the 200), a Bryston 4B and a pair of classic old Yamaha 200w. monoblocks.  The last three sounded polite (anemic) and lacking in tonal color compared to the two non-ultralinear tube amps.

Back in the 1970s, so many receivers from major companies sounded the same-distorted.  They were designed around measurements, how low can the THD and IM go, not around musical sounds.  I dreaded hearing my teen age friends playing rock.  It hurt my ears/head.  I would go home and enjoy my Yamaha integrated or Fisher 500c into a pair of Dynaco 35s, Dual 1209 and Grado cartridge.  Cheapest cabling, no vibration isolation, no acoustic treatments (nice big room 20X20X10).  That was comforting sound.