Laser and inkjet printers both have their merits when it comes to printing journal supplies. I use them both interchangeably depending on the project.
The main difference between them is that images printed on inkjet printers are generally not water resistant while laser images are in fact waterproof. This matters if you want to coffee or tea dye your paper. A page with a laser printed image can be dipped in a coffee mixture and will not bleed or run, but a typical inkjet image will.
There is one exception, however and it's the Epson Expression Home XP-430 inkjet printer which uses water resistant pigment ink; it's an amazing printer at a very affordable price point.
I also use a wide format Epson Artisan 1430 inkjet (the most recent comparable equivalent is the XP-15000) and a Canon ImageClass color laser . The wide format Epson allows me to print on 12x12 paper and uses a multi cartridge system as opposed to tri-color, which makes a huge difference in the image quality. I use only Epson brand cartridges and have found they go a very long way. This is due in part to the photo paper's quality and the ink quality, which isn't always as high in knock off cartridges. The laser toner cartridges in my Canon are also Canon and last a very long time.
There are a few ways to incorporate the antiqued look of coffee dyed paper even if you use inkjet images.