taking photos of paintings

I'm assuming you're taking images to produce prints less than A4 sheet of paper or for the web. Only if you're going to make large / full sized prints would the D5100 more likely give a noticeable difference.

I think you'll find there'll not necessarily be much difference between the two you list here for your need if your final images are going to be small (e.g. for web). The Nikon may have less noise, but will you notice? Are you planning on using the images full size? 12MP or 16MP, when printed or displayed on a monitor full size is huge. 16MP makes for massive prints. 

As you know, the D5100 is superior to the 1100D for general use, but for a one type of shot and set up, 1100D can prob handle it well enough, especially if $100 or so will affect your decision.

Two far more important things:

How you process the images the camera produces. Many people allow their camera to do the processing and shoot in JPG mode. However, that's like shooting with a Polaroid camera. If you shoot in RAW format you'll have control to ensure that your images are accurate to the colours, particularly since automatic white balance (AUTO WB) may not be accurate and you cannot truly correct this if you do not shoot in RAW. Same goes for contrast, micro contrast, sharpness etc. If accuracy is important, shooting RAW is important. You will need a computer and software to edit the RAW images and to generate the JPG images

How you shoot. The key is to have a stable tripod, shooting at ISO100 and a sharp aperture, typically around f/5.6 to f/8 depending on the lens you have. An 18-55mm kit lens would be fine, I'd recommend a 50mm f/1.8 for better results on a budget. Enable mirror up or exposure delay mode and set a timer to reduce blur (if the camera has those features). Those would give you most likely give you near enough optimum results putting aside the lighting you use. The tripod would ensure you do not introduce camera shake as you'll most likely have a reasonably long shutter speed (long enough to make handholding the camera impossible without introducing blur from shake). A tripod or other camera support must be solid, not a cheap plastic thin aluminium thing. 

In other words, if you have such a specific brief for what you need and you don't plan on printing big posters of the images, then I don't think the choice of camera is as big as the choice of how you use it. 

Better RAW quality, better low-light performance, more pixels, lower noise, better in general.

In my opinion it is worth spending a little more on this.

Draga Dan, daca tot ceea ce doresti de la camera este sa faci poze la picturi, si eventual ocazional la prieteni si familie, nu ai nevoie de un dslr. Poti cumpara un point adn shoot accesibil ca pret si pozele tale o sa exprime fidel realitatea. Insa daca vrei sa incepi sa fotografiezi sub aspect semi-pro sau doresti sa oferi o perspectiva mai diversificata unui tablou, sau oricarui alt subiect atunci ai nevoie de un dslr. D5100 nu este in aceeasi liga cu eos 1100d. Trecerea de la camerele comerciale la dslr este uneori greoaie, iar recomandarea mea este, daca nu ai o pasiune pentru fotografie, nu se justifica investitia. Eu detin mai multe aparate foto, printre care si un d5100 si iti spun sincer, poate sa faca poze foarte proaste dar si foare reusite, ceea ce depinde de tine ca fotograf, in spatele unei fotografii reusite se afla multa matematica si fizica... De la calcularea logaritmica a distantei focale, la expunerea corecta, la decizia triunghiulara a bazei iso, shutter si aperture. Multa multa matematica. La point and shoot, il pui pe automat, portret, landscape, si face ceea ce face un dslr bine setat.... Iti reda fidel realitatea. Id meu de mess este gheorghies_razvan , daca vrei vb sau mai ai intrebari.