Unless you're dealing with a really ancient system (for example, something running an 80386) or have hardware that only works with an older kernel version (and the systems you describe meet neither criteria), you should always use the newest version of Linux you can get, as it will almost always be more secure and will usually perform better.
Now, as far as your performance complaints, that's not all that unexpected. Dell Inspiron and Acer Aspire One systems are budget systems, so they're already not going to be high performance, and on top of that you're talking about ones three quarters of a decade old. Even a 300 USD laptop from last year is going to get better performance than those, regardless of what you're running on them. Most likely, both have single or at most double core CPU's running at less than 2GHz, low-end DDR2 memory, and cheap hard drives that are at this point beyond their life expectancy. Note also that LibreOffice is not a particularly good piece of software in terms of performance (try Abiword and Gnumeric if you can get away with just using a word processor and spreadsheet software), and Chrome is also notoriously memory hungry (Midori is a decent lightweight browser option).
You may be able to improve things by replacing the hard drives with SSD's (assuming they're actually SATA drives and not mini-PATA), and if you're really lucky you might be able to replace the wireless adapters (though it is getting harder to find decent mini PCI-e Wifi cards). That may be enough to improve web browsing to tolerable performance levels, but you probably won't be able to do much more to improve things. You may also be able to put in some more RAM which should help significantly, but it might be difficult to find memory modules that actually work with systems that old (if it is DDR2 that they use, you may be out of luck).