That's tougher. A lot depends on if you want to upgrade your computer down the line, or if you're going to hold onto it until it's time to replace it. Upgrades tend to be best done ever few years, replacements about twice as long, winds up costing about the same. Performance wise, the FX 6300 and the i3-4150 are about even in terms of gaming, but the FX-6300 is much better for streaming and editing.
The FX family of chips are the last chips using their particular motherboards that AMD is going to release, so there isn't much of an upgrade path from the FX-6300. After jumping to an 8 core FX chip the only difference is how much it was overclocked by the factory before they shipped it out. The i3-4150 shares a motherboard type with the i5, as well as with some i7 and Xeon chips so there's a good upgrade path.
A third option, if you were willing to use MIR's or reuse your old monitor temporarily, would be to skip the i3/FX debate entirely and jump to an i5 like so:
PCPartPicker part list / Price breakdown by merchant
| Type | Item | Price |
|---|---|---|
| CPU | Intel Core i5-4460 3.2GHz Quad-Core Processor | $178.98 @ OutletPC |
| Motherboard | MSI H81M-P33 Micro ATX LGA1150 Motherboard | $44.85 @ OutletPC |
| Memory | G.Skill Ripjaws X Series 8GB (2 x 4GB) DDR3-1600 Memory | $59.99 @ Newegg |
| Storage | Seagate Barracuda 1TB 3.5" 7200RPM Internal Hard Drive | $47.89 @ OutletPC |
| Video Card | Sapphire Radeon R9 280 3GB DUAL-X Video Card | $159.99 @ Newegg |
| Case | Azza SIRIUS ATX Mid Tower Case | $34.99 @ Newegg |
| Power Supply | EVGA 500W 80+ Bronze Certified ATX Power Supply | $37.99 @ NCIX US |
| Operating System | Microsoft Windows 8.1 (OEM) (64-bit) | $87.75 @ OutletPC |
| Monitor | LG 22M35D 60Hz 22.0" Monitor | $109.98 @ NCIX US |
| Keyboard | Cooler Master CM Storm Devastator Gaming Bundle Wired Gaming Keyboard w/Optical Mouse | $27.87 @ Amazon |
| Prices include shipping, taxes, rebates, and discounts | ||
| Total (before mail-in rebates) | $860.28 | |
| Mail-in rebates | -$70.00 | |
| Total | $790.28 | |
| Generated by PCPartPicker 2015-03-07 14:09 EST-0500 |
If you were willing to reuse your monitor, keyboard, and mouse we could even get you a top of the line PC like so:
PCPartPicker part list / Price breakdown by merchant
| Type | Item | Price |
|---|---|---|
| CPU | Intel Core i5-4460 3.2GHz Quad-Core Processor | $178.98 @ OutletPC |
| Motherboard | MSI H81M-P33 Micro ATX LGA1150 Motherboard | $44.85 @ OutletPC |
| Memory | G.Skill Ripjaws X Series 8GB (2 x 4GB) DDR3-1600 Memory | $59.99 @ Newegg |
| Storage | Seagate Barracuda 1TB 3.5" 7200RPM Internal Hard Drive | $47.89 @ OutletPC |
| Video Card | XFX Radeon R9 290 4GB Double Dissipation Video Card | $252.98 @ Newegg |
| Case | Azza SIRIUS ATX Mid Tower Case | $34.99 @ Newegg |
| Power Supply | EVGA 500W 80+ Bronze Certified ATX Power Supply | $37.99 @ NCIX US |
| Operating System | Microsoft Windows 8.1 (OEM) (64-bit) | $87.75 @ OutletPC |
| Prices include shipping, taxes, rebates, and discounts | ||
| Total (before mail-in rebates) | $825.42 | |
| Mail-in rebates | -$80.00 | |
| Total | $745.42 | |
| Generated by PCPartPicker 2015-03-07 14:11 EST-0500 |
An i5-4460 and a R9 290 will max out everything, do streaming, video editing, and anything else you want to throw at it without question. That's some serious power.