[Pilotter]

Back in 1994 I bought a pair of Sennheiser HD 560 Ovation II and almost forgot about them. Recently I restarted using them with my computer and iPad via an external DAC/headphone-amp (V90-HPA Musical Fidelity). The sound quality isn't bad, but these 560 are my only reference.
My question is, has technology improved that much that investing in new phones (price up to €400) would blow away my old ones? Examples: Sennheiser 600/650, Grado 325e, AKG Q701, Beyerdynamics T90.
By the way they are for home use only and listening to jazz, jazzrock and classical. Thanks for your input!

 

[GREQ]

 has technology improved that much that investing in new phones (price up to €400) would blow away my old ones?

The short answer: No.
 
I have the older HD540 which are VERY similar to your 560's (arguably yours are better according to most opinions I've read around here, but they're pretty much siblings and are more similar than different) and I honestly think the 540 compares to most modern flagships in terms of overall detail retrieval, timbre and soundstage.
 
The only area where other headphones are clearly OBJECTIVELY better is the bass. The older Senns from this period have quite significant bass roll-off below 100Hz, which is only detrimental is you have no way of managing the sound with an equalizer or listen to bass heavy genres that benefit from some low-end grunt. 
I prefer to mod the headphones than the sound signal, and have found my HD540's have the best overall sound with Hifiman pleather earpads (but it adds a touch of honkiness to the mids), although equalizing the sub bass with the original earpads gives a better timbre and retains airiness to the sound.

This breed of sennheisers are still strong if you tweak your system around them, and should suit your preferred genres. 
Only consider investing in another headphone if you feel that the bass response is lacking in volume, since these headphones excel in every other aspect even by modern standards.
The only headphone I would consider directly replacing the HD540 with is the HD650.