Its time to retake control of your Ipad! :) I am super-interested in computer game thingies, so lets see if I can help you.
For 6yo, I would recommend a Nintendo DS. They are ideal for this age range: bright, colourful hardware and games, very easy to use, and quite sturdy little units (it can be dropped off the end of the kitchen table with no ill effects!) The DS will grow with them as they age, its not one of those things that they decide is "babyish" and is likely to be a device that is also owned by their friends, allowing them to play together and be social. A DS Lite is the older model, but with plenty of options for games. The current generation are the DSi, and the 3DS, which has 3D graphics that stand out the screen. Nintendo's own website has a handy comparison chart for you to decide which one suits you best.
I would not recommend a Playstation Vita, the primary reason being that it will simply be too big for their hands. Its uncomfortable for me, and Im twenty, with great dinnerplates for hands! Its a much more adult device, I would be looking at maybe a 12 or 13 yo. An older child would get much more out the features, eg the graphics, big glass screen and 3 different input methods. I feel a 6yo would struggle with a Vita.
Ipod touch would be a possibility, because you are familiar with the hardware (from owning an ipad). The games are cheaper, and you have additional functionality such as music and so on, buuuut, you will get sucked into having to upgrade frequently when your children cotten on to next-Apple-product-itis, and Apple products are pretty delicate when knocked on the corners. You also need to go through the rigmarole of keeping it up to date and locking down the controls to prevent in-app purchases backrupting your credit card!
A Gameboy is a vintage option! Older equipment is cheaper, but you will have all the associated problems of trying to find games for it, Ebay & Charity shops are your friend and I worry that after all that work sourcing games, at around 7 or 8, they will start wanting a "proper" handheld like thier friends have.
Unfortunately, no matter which handheld you go for, you will find the games to be fairly expensive if you are used to paying £3 tops for Ipad games. £25 per game would be a good deal for a Vita or DS. If you would like some suggestions for games, I would be happy to help pick out some ideas. What kind of things do they like: builing things, puzzles, stories, animals, Disney, art? Nintendo also did a few superb quality educational games for learning foreign languages for the DS family.
Hope that helps!