fdisk vs parted
Use fdisk for drives that are < 2TB and either parted or gdisk for disk > 2TB. The actual difference has to do with the partitioning formats that these tools are manipulating.
For disks < 2TB you're often using MBR (Master Boot Record). For disks > 2TB you're using GPT (GUID Partitioning Table). Here's a good article that covers the differences as well, titled: The Differences Between MBR and GPT.
What to use?
In a nutshell you can continue to use fdisk as long as the new HDDs are < 2TB. If they're larger then you can use parted or gdisk. If you need to convert from MBR to GPT you can do so (use caution with this) using gdisk.
You can read more about gdisk here on the primary website, titled: GPT fdisk Tutorial.
Example
$ gdisk -l /dev/sdb
GPT fdisk (gdisk) version 0.8.4
Partition table scan:
MBR: protective
BSD: not present
APM: not present
GPT: present
Found valid GPT with protective MBR; using GPT.
Disk /dev/sdb: 5860533168 sectors, 2.7 TiB
Logical sector size: 512 bytes
Disk identifier (GUID): B40CXXXX-XXXX-XXXX-XXXX-XXXXXXXXXXXX
Partition table holds up to 128 entries
First usable sector is 34, last usable sector is 5860533134
Partitions will be aligned on 8-sector boundaries
Total free space is 0 sectors (0 bytes)
Number Start (sector) End (sector) Size Code Name
1 34 5860533134 2.7 TiB FD00 primary
You can also opt to use parted exclusively. It can contend with both MBR and GPT.
Example
$ parted -l
Model: ATA ST3250820AS (scsi)
Disk /dev/sda: 250GB
Sector size (logical/physical): 512B/512B
Partition Table: msdos
Number Start End Size Type File system Flags
1 32.3kB 49.4MB 49.3MB primary fat16
2 49.4MB 2204MB 2155MB primary fat32
3 2204MB 2410MB 206MB primary ext3 boot
4 2410MB 250GB 248GB extended
5 2410MB 2517MB 107MB logical ext3
6 2517MB 250GB 247GB logical lvm
Model: ATA ST3000DM001-1CH1 (scsi)
Disk /dev/sdb: 3001GB
Sector size (logical/physical): 512B/512B
Partition Table: gpt
Number Start End Size File system Name Flags
1 17.4kB 3001GB 3001GB primary raid
Model: ATA ST3000DM001-1CH1 (scsi)
Disk /dev/sdc: 3001GB
Sector size (logical/physical): 512B/512B
Partition Table: gpt
Number Start End Size File system Name Flags
1 17.4kB 3001GB 3001GB primary raid
NOTE: Here you can see I have a 250GB MBR drive (/dev/sda) along with 2 3TB GPT drives (/dev/sdb & /dev/sdc).
The primary reason to use gparted or parted is if the new disk is bigger than 2TB. But you probably will not be able to effectively set that up from a 32 bit system.
If you want to run the new disk from your old system. Stay with a disk smaller than 2TB. You should be able to partition, format and run that from you old computer using fdisk for partitioning.
If you want to buy a bigger disk as 2TB, then partition it from the new system with parted. New installation CDs nowadays work with parted (or its library) by default to prevent problems with big disks.
In my experience fdisk is more powerful (especially in the advanced mode), but it can leave your disk in a somewhat weird state.
For example fdisk will allow your partitions to lie out of order unless you specifically tell it to reorder them, most other tools (and unless i'm very mistaken parted is one of them) will make assumptions that you want everything to be 'clean' once you are finished, even when you didn't expect to have some action performed.
When I write 'out of order' I mean something like this:
Device Boot Start End Blocks Id System
/dev/sda1 * 2048 24000094 11999023+ 83 Linux
/dev/sda2 24000512 48001023 12000256 83 Linux
/dev/sda3 48003070 488396799 220196865 5 Extended
/dev/sda4 24000095 24000511 208+ 83 Linux
/dev/sda5 480397312 488396799 3999744 82 Linux swap / Solaris
/dev/sda6 48003072 480395263 216196096 83 Linux
Note that sda6 lies before sda5 on the disk.