It is NOT a Matter of IF they work together, of course they do, but when at the end of the Curve (Charge & Discharge) that is where the size difference becomes an issue. 280AH + 100AH will result in issues. The 280's will attempt to Backcharge the 100AH as it discharges and that has a COST... This is very easy to see as it happens. During charge is less issues because the 100AH will reach designated FULL and platean there and Amps taken will just decrease to <1A taken or even go into storage mode (pending on BMS) at which point the 280 will continue taking everything they can till it/they drecrease Amps Taken and reach full.
The Gotcha which CAN HAPPEN depends on your Charge Setup. You can never exceed 0.5C Rate of the lowest pack in the bank. For 100AH that is 50A Max while the 280AH is 140A Max Charge Rate. Technically you can push as much as 190A for One Hour to charge both up @ 0.5C but such is rarely ever done. Fortunately like Discharge, the Charging is split/shared "Proportionately" not equally relative to battery capacity rating.
Cables, Placement on DC-Busbars do play very important roles as it affects line-lost resistance which is noticeable by Lithium Batteries, unlike Lead which is in essence Brute Force tech. Cable Gauge, Grade & Lengths from BATT Terminals to Common DC Bus should be the same length.
Every crimped lug, terminal, switch etc adds resistance which is Voltage & Amperage drop. These wires should be kept close together to prevent magnetic & electrical noise. Always use High-Quality Fuses & Breakers not only because it is wise to do so, but they are also much better with regards to resistance (which makes heat and that is bad) and line losses.
The charging difference is very easy to see when you are charging. I can watch my bank charge and while the 280AH Packs may be taking 25A +/- ea the 175's will be taking 17A+/- a bit. When discharging you will also see the 100AH will output less Amps while the 280AH will be outputting more.
SOME BMS' have a Sleep / Storage Mode which can be triggered during charge, once the battery pack is fully saturated, or when discharged to Low Volt Disconnect LVD which prevents them from a Full OFF state. In that instance, the BMS wakes up to see if an incoming charge is present, if not, sleep, if yes, open to receive charge, these will cycle this way until a critical point is reached at which time they fully shutoff to protect the battery pack.
*** REMEMBER TO FUSE THE BATTERY TO THE BATTEY ! 100AH Battery should get 100A Fuse and the 280AH a 250A Fuse. Fuses will allow for a short Burst above as will the BMS' and the cells. I have 300A Fuses on the 280's and 200A on the 175AH packs.
A NOTE MANY DO NOT KNOW ABOUT !
We always talk about resistance and how it affects things,
The battery Terminals used can be Very Significant for resistance ! Lead Acid Batts use Lead Terminals which are Low Resistance and being "Brute Force" tech is not that significant at that level. No Lithium pack uses Lead Terminals and you cannot even buy them (Controlled substance in MANY MANY Places, (Lead is really Nasty Assed Crap !) ) Almost all Terminals used by us DIY Folk are made of BRASS and are often nickel plated... Brass is not the best of conductors and varies a LOT with the quality of Brass used (it is extremely recycled everywhere, get's whiter each time, as well as more brittle & increased resistance) Then depending on "what" it is plated with can also have effects which are not desirable. Chrome Plating is not equivalent to Nickle or Tin for conductivity. SOME ARE SHOCKED to see as much as 1.0V Drop just across the Battery Terminals and don't get why.... then don't want to hear it when told why.
BTW / FYI: Many Vendors include busbars with their cells. A Good Majority use CHEAP Chromed Brass Busbars which have a higher resistance while other use proper Nickel Plated Copper Busbars (more costly) with much lower resistance, while some just offer straight Copper Busbars.
* Always use the same type of busbar when assembling a pack, mixing them will skew numbers and affect the BMS (charge/discharge & alancing)
* Try to build packs in a consistent format and replace that with each added pack of same size.
* Do make every effort to use identical BMS's for all packs within a Bank. Makes managing, adjusting & monitoring easier. Also better for Fault Tolerance and Fail Over implementations.
* Check resistance through items like Battery Box Terminals. Common examples shown below.
These are from Morosso but Painless and many others are the same.
Unplated brass has lower resistance as opposed to the Chrome Plated ones.. That's right, Chrome, not Nickel.