Unfortunately there is no best model, and definitely no perfect model... The choice mostly depends on which aspect(s) of the disease you want to study. And as always, you need to use appropriate controls.
popular AD models overexpressing Abeta includes Tg2576 and 3xTg mice, among many other. However, it has been recently found that knock-in mice with humanized Aβ and tau may more faithfully model AD. Please see: http://www.alzforum.org/news/conference-coverage/next-generation-mouse-models-tau-knock-ins-and-human-chimeras
Unfortunately there is no best model, and definitely no perfect model... The choice mostly depends on which aspect(s) of the disease you want to study. And as always, you need to use appropriate controls.
Let me throw another option out for you- Down Syndrome modeling mice.
Down syndrome (DS) is CLOSELY related to Alzheimer's disease (AD). DS individuals all develop the classic plaques and tangles in addition to developing an age-related cognitive decline which is not related to their underlying DS cognitive deficits. DS is the triplication of chromosome 21, on which you can find the following triplicated genes related to AD: APP, SOD1, DYRK1 to name but a few.
The TS65Dn mouse model was developed for studying Down syndrome. This mouse carries a partial triplication of mouse chromosome 16. The portion of mouse Ch16 which is triplicated is analogous to the portion of human Ch21 thought to be most involved in AD and the cognitive effects of Down Syndrome- including the triplication of APP, SOD1, and DYRK1. These mice have a cognitive deficit early in life- similar to the humans with Down Syndrome AND they develop an additional age-related cognitive decline similar to humans with AD and older Down syndrome individuals.
The Ts65Dn mice develop age-related neuronal loss and decreased NGF expression. They over express APP and A-beta but it does not develop into classic plaques. They accumulate an extra-somatic deposit (or tangle) that contains tau, reelin, and other axonal markers. These axonal deposits appear to a part of normal aging, however the frequency of these clusters is what differentiates the AD/DS aging mouse from normally aging mice. The clusters can also be found in other AD mouse models (AD11, SAM-P8, SynGAP, 3xTgAD).
The advantage of using a Down syndrome model for studying AD is: cognitive decline emerges earlier, there are no artificial insertion of human genes, they express both cognitive and neuropathological characteristics in one model.
As previous answers pointed out, though, the "best model" depends on what aspect of AD you are studying because right now, there is no perfect mouse model, although I think the TS65Dn model is pretty good. :)
PS. Check out these articles for more info on the extra-somatic tau deposits:
The Tg-F344-AD rat model is a good one, especially if you are working with a complex behavioral repertoire (mice just can't to some of the tasks rats can). Age dependent increasees in an array of AD pathology and age dependent impairment in cognition.
You might consider Octodon degus as a good animal model for Alzheimer's since the wild type of the animals display Alzheimer's pathology. The brain pathology might be due to exposure to soil bacteria or fungi, such as streptomyces, with Abeta acting as an antimicrobial defense mechanism. There are some publications on Octodon degus that could be helpful such as this one:
Natural AD-Like Neuropathology in Octodon degus: Impaired Burrowing and Neuroinflammation.