Hope 1 is 240 lumens... with AA's. The Ayups are 340 lumens but a bit more money...
Between the two, I'd say it's a personal preference and a 'tiny' amount of space for the ayup battery....
Pro's....
Hope 1 - Take AA's (use hybrids and you are laughing), easy battery changes, and when batteries die, just get a new set, lots of power settings, all in one unit... Excellent UK support. No additional battery pack.
Ay-up - Tiny twin lamps, v bright, very neat, small battery pack, light weight,...excellent Aus Support..
Cons....
Hope 1's..... Heavier than the Ay-up, not as bright (1 LED but cheaper)
Ay-ups - Lack of different light levels, separate battery pack, bit more expensive, batteries die, then specific pack.
Both light systems are excellent, the Ay-ups are tiny, the Hope's aren't exactly big, but at least twice the size of the ay-ups....
I use two Hope 1's - just more flexibility and about the same price as the Ay-Up system...480 on max, and can use alternate flashing.....
It's personal preference... for me was the AA batteries - seen too many issues with 'specific' packs failing - AA's just bin them or upgrade, as these hybrids are very good.... and the unit is in one - so quick off. They would be better if the bracket remained on the bike, but the whole lot comes off, but it only takes about 3 seconds to fit, rather than 1....
That said, I've seen the Ay-ups, and they are so small, you'd not know they were there until switched on. If you have a clutter free bar stem, then no probs fitting the battery.....
Both very good systems - pick what suits you.............. customer service is second to none for both systems....