Now that I have 2 options for a low budget laptop:
AMD A6 1MB cache, 256GiB SSD.
AMD Ryzen3 5MB cache, 1TB HDD
Which one is likely to yield
better responsiveness in user applications (non gaming, but maybe some heavy IDEs)?
better battery backup - if there is any apparent effect.
I fear you may be asking the wrong question, and providing too little information. You have not provided sufficient information to allow a direct CPU comparison, but have a look at https://www.cpubenchmark.net/compare/AMD-A6-9225-vs-AMD-Ryzen-3-3200U/3315vs3431 for something indicative.
As a first cut approximation you can ignore the cache, as its performance is "folded in" to the CPU benchmarks. The Ryzen3 is a WAY faster CPU then the AMD A6 (Think 2-4 times the speed). Of-course, it is likely that the system will spend more time with disk IO then CPU IO, so the SSD system will likely be faster.
On the other hand, an SSD will outperform a hard drive by 1-3 order of magnitude (ie 5-100 times faster, and you are looking towards the middle upper end for an IDE where lots of small files are involved). Especially if you are moving the laptop around a lot, an SSD is more resiliant to failure then an HDD (think 10x the reliability)
You may want to compare the TDP of the CPUs - if I guessed correctly, both are 15W - which means that there will be very little difference in the runtime assuming the same size battery - on the one hand you have a faster CPU (so it uses less power to do its job), on the other hand SSDs use less power then HDDs.
If it were me, particularly bearing in mind the IDE/Development comment I would likely get the Ryzen3 system and replace the HDD with an SSD. If I could not reach for the extra cost now, I might still be inclined to buy the Ryzen 3, and then upgrade it to an SSD later on. In my mind an SSD is non-negotiable on a computer. If I had to choose between a fast system and HDD and a slow system and IDE, with no option of an upgrade, I'd go with the slow SSD based system.
